Group-based Criminal Trajectory Analysis Using Cross-validation Criteria

In this article, we discuss the challenge of determining the number of classes in a family of finite mixture models with the intent of improving the specification of latent class models for criminal trajectories. We argue that the traditional method of using either the Proc Traj or Mplus package to compute and maximize the Bayesian Information Criterion (BIC) is problematic: Proc Traj and Mplus do not always compute the MLE (and hence the BIC) accurately, and furthermore, BIC on its own does not always indicate a reasonable-seeming number of groups even when computed correctly. As an alternative, we propose the new freely available software package, crimCV, written in the R-programming language, and the methodology of cross-validation error (CVE) to determine the number of classes in a fair and reasonable way. In this article, we apply the new methodology to two samples of N = 378 and N = 386 male juvenile offenders whose criminal behavior was tracked from late childhood/early adolescence into adulthood. We show how using CVE, as implemented with crimCV, can provide valuable insight for determining the number of latent classes in these cases. These results suggest that cross-validation may represent a promising alternative to AIC or BIC for determining an optimal number of classes in finite mixture models, and in particular for setting, the number of latent classes in group-based trajectory analysis.     

Partitioned difference families and almost difference sets

Partitioned difference families (PDFs) were first studied by Ding and Yin in conjunction with the construction of constant composition codes (CCCs). In 2008, Yin et al. presented the constructions of a number of infinite classes of PDFs based on known difference sets in GF(q). In this paper, we further investigate the constructions of PDFs by using known almost difference sets in GF(q), and establish some recursive constructions of PDFs. As their applications, we also get a number of perfect difference systems of sets (DSSs) over Z_q² with q odd prime.     

Covariance analysis and associated spectra for classes of nonstationary processes

In 1951, Cramér introduced a class of nonstationary processes. This broad class of processes contains the important harmonizable and stationary classes of processes. The Cramér class can have additional structure imposed upon it through Cesàro summability considerations. These refined Cramér classes, termed (c,p)-summable Cramér, have recently been considered by Swift (in: M.M. Rao (Ed.), Real and Stochastic Analysis: Recent Advances, CRC Press, Boca Raton, FL, 1997, p. 303). In this paper, the relationship between the (c,p)-summable Cramér classes and the (KF,p) classes of processes introduced by Rao in 1985 is considered. The (KF,p) classes of processes are a generalization of the class of processes considered by Kampé de Feriet and Frenkiel. A continuity theorem for the (KF,p) classes is obtained. This result yields a spectral representation for the (KF,p) classes. Some (KF,p) class processes are shown to arise as the solution to a difference equation obtained from a linear model of a noisy communication channel.     

On improvement in estimating the population mean in simple random sampling

Kadilar and Cingi [Ratio estimators in simple random sampling, Appl. Math. Comput. 151 (3) (2004), pp. 893–902] introduced some ratio-type estimators of finite population mean under simple random sampling. Recently, Kadilar and Cingi [New ratio estimators using correlation coefficient, Interstat 4 (2006), pp. 1–11] have suggested another form of ratio-type estimators by modifying the estimator developed by Singh and Tailor [Use of known correlation coefficient in estimating the finite population mean, Stat. Transit. 6 (2003), pp. 655–560]. Kadilar and Cingi [Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett. 19 (1) (2006), pp. 75–79] have suggested yet another class of ratio-type estimators by taking a weighted average of the two known classes of estimators referenced above. In this article, we propose an alternative form of ratio-type estimators which are better than the competing ratio, regression, and other ratio-type estimators considered here. The results are also supported by the analysis of three real data sets that were considered by Kadilar and Cingi.     

Multivariate convex risk statistics with scenario analysis

Abstract

In this article, we introduce three new classes of multivariate risk statistics, which can be considered as data-based versions of multivariate risk measures. These new classes are multivariate convex risk statistics, multivariate comonotonic convex risk statistics and multivariate empirical-law-invariant convex risk statistics, respectively. Representation results are provided. The arguments of proofs are mainly developed by ourselves. It turns out that all the relevant existing results in the literature are special cases of those obtained in this article.     

Stochastic Aging Classes for the Maximum Statistic from Friday and Patil Bivariate Exponential Distribution Family

Friday and Patil bivariate exponential (FPBVE) distribution family is one of the most flexible bivariate exponential distributions in the literature; among others, it contains the bivariate exponential models due to Freund, Marshall–Olkin, Block–Basu, and Proschan–Sullo as particular cases. In this article, we discuss the stochastic aging of the maximum statistic from FPBVE model in according to the log-concavity of its density function, i.e., in the increasing or decreasing likelihood ratio classes (ILR or DLR), and consequently in the IFR and DFR classes. Furthermore, a kind of DFR distributions which are not DLR is derived from our classification.     

Preservation of some reliability properties by certain record statistics

Record values are closely connected with the occurrence times of a corresponding non-homogeneous Poisson process and in reliability theory, they are used in shock models. In this paper, first, some distribution properties of current records are presented. It is then shown that the hazard (reversed hazard) function of the upper (lower) current records can be expressed in terms of the hazard (reversed hazard) function of the parent distribution. Some reliability relationships between the original variable X and the corresponding current records and with record ranges are established. Also, preservation of some uncertainty measure based on current records is discussed.     

《货币与金融统计编制指南(CGMFS2008)》的比较与思考

 2000年货币与金融统计领域的第一部国际标准《货币与金融统计手册（2000）》出台,时隔八年之后,国际货币基金组织又颁布了更具操作性的《货币与金融统计编制指南（2008）》。通过新旧两个版本的比较,本文对总体框架与主要内容的变化进行了述评,进而结合中国实际提出了加强研究并做好准备的建议。     

On Two General Classes of Discrete Bivariate Distributions

In this article, we develop two general classes of discrete bivariate distributions. We derive general formulas for the joint distributions belonging to the classes. The obtained formulas for the joint distributions are very general in the sense that new families of distributions can be generated just by specifying the “baseline seed distributions.” The dependence structures of the bivariate distributions belonging to the proposed classes, along with basic statistical properties, are also discussed. New families of discrete bivariate distributions are generated from the classes. Furthermore, to assess the usefulness of the proposed classes, two discrete bivariate distributions generated from the classes are applied to analyze a real dataset and the results are compared with those obtained from conventional models.     

国际GFP统计规则调整对中国经常账户的影响

2008年IMF发布的《国际收支与国际投资手册》（第六版）对国际加工贸易（Goods for Processing,GFP）中的项目统计进行了调整。由于我国对外贸易中GFP所占的比重较高,因此此次调整对我国国际收支平衡表中的经常项目将产生较大影响。本文通过对GFP几种主要类型的分析,探讨了这种调整分别对我国经常项目统计产生的影响。     

Finding 'superclassifications' with an acceptable misclassification rate

Cluster analysis methods are based on measures of 'distance' between objects. Sometimes the objects have an internal structure, and use of this can be made when defining such distances. This leads to non-standard cluster analysis methods. We illustrate with an application in which the objects are themselves classes and the aim is to produce clusters of classes which minimize the error rate of a supervised classification rule. For supervised classification problems with more than a handful of classes, there may exist groups of classes which are well separated from other groups, even though individual classes are not all well separated. In such cases, the overall misclassification rate is a crude measure of performance and more subtle measures, taking note of subgroup separation, are desirable. The fact that points can be assigned accurately to groups, if not to individual classes, can sometimes be practically useful.     

Generalized Systematic Sampling

In this paper, we introduce a new systematic sampling design, called a Generalized Systematic Sampling (GSS), for estimation of finite population mean. The proposed design is found to be better than Simple Random Sampling (SRS) and the generalization of the several existing systematic sampling schemes such as, Linear Systematic Sampling (LSS), Diagonal Systematic Sampling (DSS), and Generalized Diagonal Systematic Sampling (GDSS). All of these designs become special cases of the proposed design.     

Nonisomorphic complete sets of orthogonal f-squares and hadamard matrices

Five nonisomorphic classes of Hadamard matrices of order 16 were given by Hall (1961). Three of these Hadamard classes have a 4 ×4 row and column structure; they generate three nonisomorphic complete sets of nine orthogonal F(4;2,2)-squares, one of which shows a previously unreported pattern. The remaining two Hadamard classes do not produce complete sets of F-squares, Each of the five Hadamard classes corresponds to a distinct set of single-degree-of-freedom contrasts in an analysis of variance.     

Parameter estimation in nonlinear regression models 1

Fisher information contained in record values, inter-record times and their concomitants from a sample of fixed size is derived in general and explicit expressions are deduced for some specific known bivariate classes of distributions. A comparison between fixed sampling and inverse sampling schemes with equal number of records and concomitants is also carried out. We also consider parameter estimation based on bivariate records and a small simulation study is done.     

Estimation Methods of the Long Memory Parameter: Monte Carlo Analysis and Application

Since the seminal paper of Granger & Joyeux (1980), the concept of a long memory has focused the attention of many statisticians and econometricians trying to model and measure the persistence of stationary processes. Many methods for estimating d, the long-range dependence parameter, have been suggested since the work of Hurst (1951). They can be summarized in three classes: the heuristic methods, the semi-parametric methods and the maximum likelihood methods. In this paper, we try by simulation, to verify the two main properties of [dcirc]: the consistency and the asymptotic normality. Hence, it is very important for practitioners to compare the performance of the various classes of estimators. The results indicate that only the semi-parametric and the maximum likelihood methods can give good estimators. They also suggest that the AR component of the ARFIMA (1, d, 0) process has an important impact on the properties of the different estimators and that the Whittle method is the best one, since it has the small mean squared error. We finally carry out an empirical application using the monthly seasonally adjusted US Inflation series, in order to illustrate the usefulness of the different estimation methods in the context of using real data.     

Almost unbiased ratio and product estimators based on interpenetrating subsamples

This paper proposes two classes of almost unbiased ratio and product estimators, in the case of interpenetrating subsample designs, which include the estimators considered by earlier authors. Several other almost unbiased ratio and product estimatbrs are given whlch are particular members of the proposed classes of estimators. Optimum estimators are also identified in these classes.     

Local Adaptivity of Kernel Estimates with Plug-in Local Bandwidth Selectors

In non-parametric function estimation selection of a smoothing parameter is one of the most important issues. The performance of smoothing techniques depends highly on the choice of this parameter. Preferably the bandwidth should be determined via a data-driven procedure. In this paper we consider kernel estimators in a white noise model, and investigate whether locally adaptive plug-in bandwidths can achieve optimal global rates of convergence. We consider various classes of functions: Sobolev classes, bounded variation function classes, classes of convex functions and classes of monotone functions. We study the situations of pilot estimation with oversmoothing and without oversmoothing. Our main finding is that simple local plug-in bandwidth selectors can adapt to spatial inhomogeneity of the regression function as long as there are no local oscillations of high frequency. We establish the pointwise asymptotic distribution of the regression estimator with local plug-in bandwidth.     

Some efficient classes of estimators of population mean in two-phase successive sampling under random non response

In this paper, an attempt has been made to present some efficient classes of estimators of population mean on current occasion in two-occasion successive sampling under random non response in two-phase setup. Effectiveness of the proposed classes of estimators has been studied under the assumptions that sampling units follow a distribution under the random non response. To check the performances, the proposed classes of estimators are compared with an estimator under the similar situation under the complete response. Results are demonstrated through empirical studies which show the reliable nature of the proposed classes of estimators. Suitable recommendations have been made to the survey practitioners.     

The Optimal Allocation Combination for the One-Sided Sequential Screening Procedure Based on the Individual Misclassification Error

In this article, the expected total costs of three kinds of quality cost functions for the one-sided sequential screening procedure based on the individual misclassification error are obtained, where the expected total cost is the sum of the expected cost of inspection, the expected cost of rejection, and the expected cost of quality. The computational formulas for three kinds of expected total costs are derived when k screening variables are allocated into r stages. The optimal allocation combination is determined based on the criterion of minimum expected total cost. At last, we give one example to illustrate the selection of the optimal allocation combination for the sequential screening procedure.